All varieties of orthogroups.
An associative operator on the lattice of varieties of inverse semigroups.
An example of the limit variety of semigroups.
An introduction to -graphs, a graph-theoretic representation of natural numbers.
Bands of Groups with Universal Properties.
Bases for certain varieties of completely regular semigroups
Completely regular semigroups equipped with the unary operation of inversion within their maximal subgroups form a variety, denoted by . The lattice of subvarieties of is denoted by . For each variety in an -subsemilattice of , we construct at least one basis of identities, and for some important varieties, several. We single out certain remarkable types of bases of general interest. As an application for the local relation , we construct -classes of all varieties in . Two figures illustrate...
Binary relations on the monoid of V-proper hypersubstitutions
In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.
Certain Rees matrix semigroups with universal properties.
Characterizing pure, cryptic and Clifford inverse semigroups
An inverse semigroup is pure if , , implies ; it is cryptic if Green’s relation on is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize groups and...
Commutativity of Operators on the Lattice of Existence Varieties.
Completely regular semigroup varieties generated by Mal'cev products with groups.
Completely regular semigroups as semigroups of partial transformations.
Completely simple and completely 0-simple identities.
Complexity of hypersubstitutions and lattices of varieties
Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and left-seminearrings of hypersubstitutions can be used to describe complete sublattices of the lattice of all varieties of algebras of a given type. The complexity...
Connections between left adequate semigroups and ...-semigroups.
Contractive representations: A family of inverse monoids and semigroups and finite R-classes.
Corrigendum to "Operators and products in the lattice of existence varieties of regular semigroups".
Corrigendum to "The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups".
Critical theories of varieties of semigroups satisfying a permutation identity.
Decidability of equational theories of coverings of semigroup varieties.